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Math Help - Urgent!!!help with attempted questions - urgent

  1. #1
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    Urgent!!!help with attempted questions - urgent

    I am so rusty, I need help solving these problems. I attempted some and i have my attempted solutions at the end of each question. However, im not sure about them. Can anyone show me step by step solutions to these? Can anyone help please? It is so URGENT!!! I'd greatly appreciate it. Thanks



    1: 200 internet connections were tested for their quality of service
    (number of packets dropped) and speed (high and low). The data is as shown:


    High Quality Low Quality

    High Speed 140 18

    Low Speed 32 10

    If we define A={a connection is of high quality}, B={a connection has high speed}
    find P(A), P(B) and P(A and B) and determine if A and B are independent events.

    My attempt
    P(A) = (140 +32)/200
    P(B) = (140 +18)/200
    P(A n B) = the product of the two


    2: In an 8 bit word each bit is equally likely to be 0 or 1.
    (a) Find the probability that all bits are 1's.
    (b) Find the probability that all bits are 0's.
    (c) Find the probability that exactly 1 bit is 1 and 7 bits are 0's.

    My Attempt
    (a)8/256
    (b)8/256


    3: In a packet switched network there are two types of routes: congested
    and not congested. Assume that 30% of the routes are congested.
    The probability of a dropped packet is 0.001 when the connection is not
    congested, and the probability is 0.01 when the connection is congested.
    (a) Find the probability that a packet is dropped.
    (b) If a packet is dropped what is the probability that it was sent on
    a congested route?
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  2. #2
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    Thanks
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    1. P(A n B) = the product of the two
    Why? That question was two parts. Need to justify this step; by using the product of the two, you are making the assumption that the two events are independent.

    (c) Find the probability that exactly 1 bit is 1 and 7 bits are 0's.
    You need to use the binomial distribution on this one. You may attempt an answer using the product of the eight individual events, and find it is no different than the probability you found in a or b. This is a wrong assumption though. Because the probability of a 1 or a 0 is 0.5, there is symettry here. Are you familiar with the binomial formula?

    (a) Find the probability that a packet is dropped.
    You need to use Bayes Theorem here. We can say that our events A are of the type of route: congested and not congested. This means our congested can be seen as A1 and A2. These events are EXHAUSTIVE, meaning they cover the entire sample space. However we can have a subevent B which touches are evetns A1 and A2 and is the event that a packet is dropped. Notice that theres no B1 and B2 - just B. Either the packet is dropped or its not dropped. Given that The route is not congested, there is a 0.001 chance of losing a packet; and given that the route is congest, there is a 0.01 chance of a packet. In English: 0.001 of 70% of routes will drop a packet, and 0.01 of 30% of the routes will drop a packet. This is our new sample space: the space of dropped packets. Armed with this, and knowing it follows Bayes, see if you can work the rest of the problem.
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  3. #3
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    Hi ANDS So how do i mathematically determine that the events are independent instead of making an assumption? I will look at how to go about the binomial and bayem's theorem in the morning. I'm not sure i totally understand it yet but i can give a feedback and let you know if i understand the concepts or not...thanks
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